Croissance des Solutions des D-Modules algébriques holonomes – (Growth of solutions of holonomic algebraic D-modules)

We show that the cohomology of complexes of solutions of exponantial type associated to holonomic algebraic D-modules is constructible. We also compute the Euler–Poincaré index of such complexes.     

若干点不交的n阶路的并图的非正规强度

本文研究了若干点不交的n阶路的并图的非正规强度.利用构造矩阵的方法,获得了若干点不交的n阶路的并图(n=1(mod 4))的非正规强度,推广了文献[5]中的结论.     

Edge irregular total labellings for graphs of linear size

As an edge variant of the well-known irregularity strength of a graph G=(V,E) we investigate edge irregular total labellings, i.e. functions f:V∪E→{1,2,…,k} such that f(u)+f(uv)+f(v)≠f(u^′)+f(u^′v^′)+f(v^′) for every pair of different edges uv,u^′v^′∈E. The smallest possible k is the total edge irregularity strength of G. Confirming a conjecture by Ivan?o and Jendrol’ for a large class of graphs we prove that the natural lower bound is tight for every graph of order n, size m and maximum degree Δ with m>111000Δ. This also implies that the probability that a random graph from G(n,p(n)) satisfies the Ivan?o-Jendrol’ Conjecture tends to 1 as n→∞ for all functions p∈[0,1]^N. Furthermore, we prove that is an upper bound for every graph G of order n and size m≥3 whose edges are not all incident to a single vertex.     

On the total vertex irregularity strength of trees

A vertex irregular total k-labelling λ:V(G)∪E(G)?{1,2,…,k} of a graph G is a labelling of vertices and edges of G done in such a way that for any different vertices x and y, their weights wt(x) and wt(y) are distinct. The weight wt(x) of a vertex x is the sum of the label of x and the labels of all edges incident with x. The minimum k for which a graph G has a vertex irregular total k-labelling is called the total vertex irregularity strength of G, denoted by . In this paper, we determine the total vertex irregularity strength of trees.     

Distant total irregularity strength of graphs via random vertex ordering

Let $c:V\cup E\to \{1,2,\dots ,k\}$ be a (not necessarily proper) total colouring of a graph $G=(V,E)$ with maximum degree $\Delta$. Two vertices $u,v\in V$ are sum distinguished if they differ with respect to sums of their incident colours, i.e. $c\left(u\right)+{\sum }_{e?u}c\left(e\right)\ne c\left(v\right)+{\sum }_{e?v}c\left(e\right)$. The least integer $k$ admitting such colouring $c$ under which every $u,v\in V$ at distance $1\le d(u,v)\le r$ in $G$ are sum distinguished is denoted by ${\mathrm{ts}}_r\left(G\right)$. Such graph invariants link the concept of the total vertex irregularity strength of graphs with so-called 1-2-Conjecture, whose concern is the case of $r=1$. Within this paper we combine probabilistic approach with purely combinatorial one in order to prove that ${\mathrm{ts}}_r\left(G\right)\le (2+o\left(1\right)){\Delta }^{r?1}$ for every integer $r\ge 2$ and each graph $G$, thus improving the previously best result: ${\mathrm{ts}}_r\left(G\right)\le 3{\Delta }^{r?1}$.     

Vanishing Cycles of Irregular D-Modules

Considering a holonomic -module and a hypersurface, we define a finite family of -modules on the hypersurface which we call modules of vanishing cycles. The first one had been previously defined and corresponds to formal solutions. The last one corresponds, via Riemann-Hilbert, to the geometric vanishing cycles of Grothendieck-Deligne. For regular holonomic -modules there is only one sheaf and for non regular modules the sheaves of vanishing cycles control the growth and the index of solutions. Our results extend to non holonomic modules under some hypothesis.     

Image inverse d'un D-module and Newton Polygon)

We show that, under conditions about the microcharacteristic variety of a coherent -module, the Cauchy problem is well-posed in the spaces of formal power series with Gevrey growth. We deduce that the filtration of the Irregularity Sheaf of a holonomic -module, which we defined in a previous work, is preserved under inverse image if some rather general geometric conditions are fullfilled.     

武汉GPS台网观测的电离层不规则结构漂移

利用2004年11月上旬强磁暴期间电离层总电子含量（QTEC）和电波闪烁武汉GPS监测台网的观测数据,采用小波去噪和互相关技术,计算了电离层不规则结构的视在纬圈漂移速度.结果表明,在11月10日夜间,各种尺度不规则结构的存在使L-波段闪烁活动与QTEC起伏均显著增强,振幅闪烁指数（S4）最大达到1.0.根据观测台网实测的QTEC变化率（RT）,得到引起闪烁和QTEC起伏的不规则结构沿纬圈向西漂移,漂移速度从午夜前（21：30 BST）的约130 m/s下降到午夜后（02：30 BST）的40 m/s左右.该研究为电离层不规则结构纬向漂移速度的测量提供了一种可行的方法.     

氩气对乙炔预混气爆轰不稳定性的影响及量化分析

为定量研究氩气对预混气爆轰不稳定性的影响,在管径为50.8、63.5 mm的管道内对未稀释及氩气稀释(氩气的体积分数为50%、70%、85%)的C₂H₂-O₂预混气进行了实验研究和量化分析,通过烟膜轨迹获得了不同初始压力下各种预混气的爆轰结构。对烟膜图像进行数字化处理,得到了氩气稀释下C₂H₂-O₂预混气爆轰轨迹的不规则度表征:轨迹间距的柱状图、标准差曲线、自相关函数。结果表明:随着氩气体积分数的升高,三波点轨迹愈加规则,不稳定性在爆轰自持传播过程中逐渐失去主导作用。稀释后预混气爆轰轨迹间距的柱状图和自相关函数的峰值和分布离散情况基本一致,与标准差分布一致。C₂H₂-O₂-85%Ar、C₂H₂-O₂-70%Ar、C₂H₂-O₂预混气的柱状图主胞格尺寸占比分别为33%、23%、20%,标准差分别为2.66~6.60 mm、5.37~10.96 mm、27.63~36.67 mm,自相关函数的第1个最高峰值分别高于其他峰值1/3倍、1/6倍、1/7倍。通过分析标准差数据,拟合得到氩气的体积分数与不稳定度的多项式函数,为选取不稳定度和氩气稀释浓度提供了依据。     

列车运行下环形轨道模型振动试验分析

搭建了环形轨道振动试验平台,开展环形轨道振动试验、轨面不平顺振动试验研究。采用INV3062T信号采集仪和INV-9828加速度传感器分别对轨道的横向响应(道床)、纵向响应(轨腰)、轨道表面和扣件支撑处进行加速度信号采集。通过凸起模拟了轨道不平顺,试验分析了轨面不平顺对钢轨动态响应的影响。分析了速度对横波、纵波和轨面不平顺的影响。结果表明:轨道横向振动幅值远大于纵向振动;相邻扣件中点处的振动响应大于扣件处;轨面不平顺会使振动响应增大甚至引起跳动;随着速度的增大,轨道振动位移响应呈上升趋势。